Area under the trignometric curve!

If \( (a, 0) ; a > 0 \) is the point where the curve \( y = \sin(2x) - \sqrt{3} \sin(x) \) cuts the x-axis and A is the area bounded by this part of the curve , the origin and positive x-axis , then find the value of : \[ 4A + 8 \cos(a) \]